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Fulham, who are eight points clear of the relegation zone, started brightly but Hugo Rodallega and Fernando Amorebieta, making his first appearance in over four months following a knee injury, each sent headers over the crossbar.
Ross McCormack saw a near-post drive kept out by Artur Boruc, but Bournemouth soon began knocking on the door themselves as Marc Pugh's fine curling effort drew a full-stretch save out of Marcus Bettinelli.
Amorebieta and Ryan Tunnicliffe had to produce desperate clearances from inside the six-yard box during a manic goalmouth scramble, but Bournemouth were not to be denied on their next attack as Pitman put them ahead.
The striker, only playing due to an injury to midweek match-winner Yann Kermorgant, struck left-footed beyond Bettinelli from 12 yards after peeling off his marker to collect a cross from overlapping left-back Charlie Daniels.
Bournemouth's second came from the opposite flank as Simon Francis's run created space for Ritchie to cut inside and bag his 10th of the season, via the aid of a Nikolay Bodurov deflection which took his shot into the bottom corner.
Victory tonight would see Eddie Howe's side climb from fourth to top, above Middlesbrough on goal difference.